For many years, the Wall Street Journal editorialized in favor of a five word Amendment to the U.S. Constitution: "There shall be open borders." So, I've long been interested in trying to estimate just how many people would move to the U.S. if this highly respectable policy recommendation were ever actually implemented. 

George Borjas pointed out that about 1/4th of all Puerto Ricans moved to the U.S. mainland after open borders started. The flow was only slowed by granting immense tax breaks to American companies who set up shop in Puerto Rico.

Even without open borders, over one-fifth of all Mexicans in the world live in the U.S.

And, as I pointed out in VDARE in 2005, about five billion people live in countries with lower average per capita GDPs than Mexico. 

So, open borders advocates ought to at least provide us with an estimate of what fraction of that five billion they would expect to immigrate here (assuming, for the sake of argument, that the effects of open borders wouldn't diminish the appeal of the United States to immigrants, which it no doubt would).

An article in the New York Times provides another test case of how many people would leave even a far distant country to move to the U.S. under a system of open borders: the Marshall Islands of the Pacific:

... the number of Marshallese [in the U.S.] is likely to grow. The islands and the United States have been intertwined since World War II. The United States has detonated at least 67 nuclear bombs in its 750,000-square-mile territory. The radioactive fallout rendered some islands uninhabitable. And United States military operations there are powered by American processed food, beloved by locals but blamed for the explosion in diabetes. 

A 1986 compact gave the United States continued military access, while the Marshallese got the right to work and live in the United States indefinitely without visas. More than a third of the Marshallese — about 20,000 — have seized the opportunity.